# What did Karman's original “Karman line” calculations look like?

Looking for the atmospheric parameters (density for example) and vehicle parameters (CL for example) as well as formulae that were used in the original calculation. Primary sources strongly preferred, as the writeups seen around the interwebs are quite inconsistent.

• I found this transcript of an interesting 1962 interview of von Kármán in his Pasadena, CA home, in the only post in hsm.stackexchange.com that contains a reference to him. – uhoh Oct 17 '18 at 14:34
• Where the velocity required for lift generation is greater than orbital velocity?! Isn't that the definition. Checking in Wikipedia, there is one that goes like "In the final chapter of his autobiography Kármán addresses the issue of the edge of outer space: Where space begins…can actually be determined by the speed of the space vehicle and its altitude above the earth." en.wikipedia.org/wiki/K%C3%A1rm%C3%A1n_line?wprov=sfla1. – karthikeyan Oct 17 '18 at 18:20
• @karthikeyan I'm aware of the definition in wikipedia. The question is not asking about the definition of the line, but about the original calculations used to come up with the definition. – Organic Marble Oct 17 '18 at 18:24

This is an interesting question and something I had never considered before.. and I think that's kind of the point. The Karman Line has been taken as a fairly universal boundary of space (in the US at least) seemingly without question. Recently, however there has been a fair amount of discussion about redefining the Karman Line. I won't go into discussion on this as it has already been addressed in this question and in a video by Scott Manley.

It appears as though the definition of the Karman line arose during a conference discussion, rather than some published paper. The quote below is from "The edge of space: Revisiting the Karman Line" by Jonathan McDowell.

The ‘von Karman line’ appears to be what mathematicians refer to as a ‘folk theorem’, arising out of a conference discussion but never formally published by him. It was fleshed out in later publications, especially in the influential work of Haley (1963 3) and there is some justification for calling it the ‘von Karman-Haley line’.

von Karman's argument was that the space boundary should be defined where forces due to orbital dynamics exceed aerodynamic forces. A rough order of magnitude argument was used to show that this was at of order 100 km (as opposed to 10 km or 1000 km), but in reality the von Karman criterion defines a line whose altitude varies with position and time (because of variations in atmospheric density due to solar activity) and with the lift coefficient of the spacecraft.

As a result, finding the primary source that you are looking for may not be possible. The closest that I think you will come is Haley's publication which is referenced in the above quote: Space Law and Government.

It's important to note, however, that exact values for atmospheric properties or vehicle parameters aren't generally associated with the definition of the Karman Line. The Karman Line is primarily defined for regulatory convenience, rather than any engineering purposes. In fact, the solar cycle changes the properties of the upper atmosphere so significantly that any accurate definition based on density, etc. would change by 10's of kilometers as solar activity changes.

Another issue is the variety of spacecraft designs; if, as von Karman argued, space was defined where forces due to orbital dynamics exceeded aerodynamic forces, the line would be defined differently each spacecraft. Further, it could even be defined differently for the various orbits and attitudes of the spacecraft.

• The more I learn about this, the more arbitrary it seems. There's nothing wrong with an arbitrary limit per se, but the next time someone tries to foist that "velocity required for lift" definition on me, they'll be met with a "citation needed" response. – Organic Marble Dec 23 '18 at 4:52
• @OrganicMarble note that the word "limit" doesn't appear anywhere in the answer; definitions can be as arbitrary as they like, their acceptance determined by practical utility or popularity. – uhoh Dec 23 '18 at 4:56
• Limit, line, it's all arbitrary. I'm declaring the Uhoh Line as the maximum number of questions that can be asked about the Karman Line! – Organic Marble Dec 23 '18 at 5:00
• So Von Kármán argued space is where orbital forces exceed aerodynamical forces. Isn't that the same as "where the centrifugal force exceeds the lift force ? – Cornelisinspace Dec 23 '18 at 12:23
• It would seem that reading this there is sensible reasoning in it - it's basically asking where that one force becomes so weak that by the time you're moving fast enough to exploit it, another one (centrifugal force, from your point of view) becomes large enough that it suffices to achieve the job you were intending to achieve. But that this doesn't define an entirely sharp and unambiguous line, so we still have to arbitrate a bit within the suggested fuzzy region with some reasonable parameters, and so pick 100 km, because it both kinda approximates the middle and is a nice round number. – The_Sympathizer Dec 25 '18 at 0:32